Zusammenfassung
We study the stability and dynamics of an ultra-cold bosonic gas trapped in a
toroidal geometry and driven by rotation, in the absence of dissipation. We
first delineate, via the Bogoliubov mode expansion, the regions of stability
and the nature of instabilities of the system for both replusive and attractive
interaction strengths. To study the response of the system to variations in the
rotation rate, we introduce a "disorder" potential, breaking the rotational
symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is
slowly varied and find forced tunneling between the system's eigenstates. The
non-adiabaticity is signaled by the appearance of a swallow-tail loop in the
lowest-energy level, a general sign of hysteresis. Then, we show that this
system is in one-to-one correspondence with a trapped gas in a double-well
potential and thus exhibits macroscopic quantum self-trapping. Finally, we show
that self-trapping is a direct manifestation of the behavior of the
lowest-energy level.
Nutzer